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Asymmetric steering in coherent transport of atomic population with a three-well Bose–Hubbard model

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Abstract

We analyze the Einstein–Podolsky–Rosen (EPR) steering properties in a three-well Bose–Hubbard model under the mechanism of coherent transport of atomic population (CTAP). This process, also known as transport without transit (TWT), transfers condensed atoms from one well of a lattice potential to another, nonadjacent well, without macroscopic occupation of the middle well. The dynamics and entanglement properties of this system have previously been analyzed and shown to be dependent on the initial quantum state of the atoms in the first well. In this work we utilize the phase-space method of stochastic integration in the positive-P representation. The system demonstrated inseparability between the wells for Fock initial states, and we show that steering is also found only for an initial Fock state. Depending on how we write our steering inequalities, steering is seen at different times, showing a basic asymmetry. This means that for part of the evolution, Alice can steer Bob but not vice versa. After the midpoint of the population transfer, this situation reverses.

© 2015 Optical Society of America

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